LMI-based Data-Driven Robust Model Predictive Control

Abstract

Predictive control, which is widely used currently, bases on a model of the system to compute the applied input optimizing the future system behavior. If the nominal models are not given or are uncertain, data-driven model predictive control approaches can be employed, where control input is directly obtained from past measured trajectories. Using a data informativity framework and Finsler's lemma, we propose a data-driven robust linear matrix inequality-based model predictive control scheme that considers input and state constraints for linear parameter-varying systems and Lur'e-type nonlinear systems. Using these data, we formulate the problem as a semi-definite optimization problem, whose solution provides the matrix gain for the linear feedback, while the decisive variables are independent of the length of the measurement data. The designed controller stabilizes the closed-loop system asymptotically and guarantees constraint satisfaction. Numerical examples are conducted to illustrate the method.